Step 1: Iron + adhesive veneer

First, remove the plastic shell of your old USB.
Cut the shape you want in the adhesive veneer sheet.
Put the USB drive in between the two sheets. Sticky sides facing the pc-board.
Iron the edges until the merge.
Repeat for the cap.
Sand down the excess glue and wood for a sharp edge.
You are done!

Step 2: Experience

It might take a few tries before you get the design you want. Make sure not to make it too wide or you'll probably end-up hiding the other computer's inputs.

i think a more rugged and a better looking version is to make 2 halves of a USB case "shell" then glue them together on the sides using wood glue or epoxy, then placing the USB inside and securing with epoxy